Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 12}$ ${3x-2y = -7}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $5x = 5$ $\dfrac{5x}{{5}} = \dfrac{5}{{5}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x+2y = 12}\thinspace$ to find $y$ ${2}{(1)}{ + 2y = 12}$ $2+2y = 12$ $2{-2} + 2y = 12{-2}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 1}$ into $\thinspace {3x-2y = -7}\thinspace$ and get the same answer for $y$ : ${3}{(1)}{ - 2y = -7}$ ${y = 5}$